Texture analysis of breast ultrasound images is widely used in the tissue characterization of breast tumors, as the texture features are closely connected to the scattering patterns and microstructures of the tumors. H-scan imaging is a novel ultrasound imaging method to differentiate the backscattering patterns inside different tissue structures. In this work, the feasibility of H-scan image texture analysis for the characterization of breast tumors is assessed. Five texture features (Contrast, Energy, Entropy, Homogeneity, and Correlation) are obtained from the H-scan images based on the Open Access Series of Breast Ultrasonic Data (OASBUD) involving 100 breast tumors of 78 female patients. Texture analysis results demonstrated significant differences (p<0.05) between benign and malignant breast tumors for the selected features derived from H-scan images. Moreover, several textural features (Energy, Entropy, Correlation) from H-scan images began to show significant differences between certain BI-RADS category levels (level 4a with level 5, level 4b with level 5). In contrast, no significant difference was in the features extracted from B-scan images of the aforementioned BI-RADS category groups. Overall, this study demonstrates that texture analysis of H-scan images is helpful for characterizing breast tumors.